Environmental GIS
Nicholas A. Procopio, Ph.D, GISP
nick@drexel.edu
Ptolemy’s Projection
URL: http://www.henrydavis.com/MAPS/Ancient%20Web%2
0Pages/119G.html
The Size and Shape of the Earth

Earth’s ellipsoid is about 1/300 off from the
sphere
Clarke, Getting Started with Geographic Information
Systems, prentice-Hall, 2001
Geodetic Datum

An estimate of the ellipsoid allows
calculation of the elevation of every point
on earth, including sea level, and is often
called a datum
Geodetic Datum Definition

The National Geodectic Survey defines a
geodetic datum as “a set of constants specifying
the coordinate system used for geodetic control,
i.e., for calculating the coordinates of points on
the Earth”
• Base reference level for the third dimension of
elevation for the earth’s surface
• Can depend on the ellipsoid, the earth model, and the
definition of sea level
• Recent datums use the center of the earth as a
reference point rather than a point on the ground
surface
Geodetic Datum



Hundreds of different datums have been used to frame
position descriptions since the first estimates of the
earth's size were made
Different nations and agencies use different datums as
the basis for coordinate systems used to identify
positions in geographic information systems, precise
positioning systems, and navigation systems
Referencing geodetic coordinates to the wrong datum
can result in position errors of hundreds of meters
Importance of Datums


Referencing geodetic coordinates to the wrong
datum can result in position errors of hundreds
of meters
Different nations and agencies use different
datums as the basis for coordinate systems
used to identify positions in geographic
information systems, precise positioning
systems, and navigation systems
Variations in Datums


Elevations referenced to a sphere,
ellipsoid, geoid, or local sea level will all be
different
Even horizontal locations may vary
Clarke Ellipsoid



In 1866, the US was mapped based on an
ellipsoid measured by Sir Alexander Ross
Clarke
Ellipsoid derived from measurements taken in
Europe, Russia, India, South Africa, and Peru
The Clarke ellipsoid had an equatorial radius of
6,378,206.4 meters and a polar radius of
6,356,538.8 meters
Clarke Ellipsoid


In 1924, a simpler measure of 1/297 was
adopted as the international standard
The US adopted the older values and became
known as the North American Datum 1927 (NAD
1927)
NAD 1927


A horizontal control datum for the U.S. defined
by a location and azimuth on the Clarke
spheroid of 1866, with an origin at the survey
station Meades Ranch, Kansas
Geoidal height at Meades Ranch was assumed
to be zero
NAD 1983


Horizontal control datum for the U.S., Canada,
Mexico, and Central America, based on a
geocentric origin
Based on measurements taken in 1980 and
accepted internationally as the geodetic
reference system (GRS80 ellipsoid)
NAD 1928 vs. NAD 1983



NAD 27 based on
Clarke Ellipsoid of
1866
NAD 27 computed
with a single survey
point (Meades Ranch)
as the datum point
Difference about
300m in places



NAD 83 based on the
Geodetic Reference
System (GRS) of
1980
NAD 83 computed as
a geocentric
reference system with
no datum point
Difference about
300m in places
World Geodetic System



U.S. military references an ellipsoid known as
the GRS80 ellipsoid
Refined the values slightly in 1984 to make the
world geodetic system (WGS84)
Significant because of GPS
Vertical Datums



A level surface to which heights are
referenced
National Geodetic Vertical Datum of 1929
(NGVD 29) - vertical control datum in the U.S.
NGVD 29 is defined by the observed (fixed)
heights of MSL at 26 tide gauges and by the
set of elevations of all benchmarks resulting
from the adjustment
Vertical Datums


North American Vertical Datum of 1988
(NAVD 88) - vertical control datum est.
in 1991 by the minimum-constraint
adjustment of the Canadian-MexicanU.S. leveling observations
Held fixed the height of the primary tidal
benchmark at Father Point/Rimouski,
Quebec, Canada.
Map Projections

Cartographer’s tool for taking curved surface of
reality (the globe) and placing it on a flat surface
such as a piece of paper or a computer screen
Projection Importance



Maps are a common source of input data for a
GIS
It is not uncommon to input various maps into a
GIS that are based on individual projections
In order to maintain accuracy of the input data,
the input maps must be referenced from the
same projection
Importance of Understanding Projections



When displaying various data, it is important that
they are all referenced to the same coordinate
system
Data displayed in varying coordinate systems
will be located incorrectly relative to each other
Very important factor data accuracy is critical
Global Projections



The most complete
projection is the globe
Scale remains
constant everywhere
Little to no distortion
Map Projections


A map projection is used to portray all or part of
the round Earth on a flat surface
Every map projection will distort one or more of
the following attributes:




Shape
Area
Distance
Direction
Distortion of Map Projections



No flat map can be simultaneously conformal
(shape-preserving) and equal-area (areapreserving) in every point
In most projections, at least one specific region
(usually the center of the map) suffers little or no
distortion
If the represented region is small enough (and if
necessary suitably translated in an oblique map),
the projection choice may be of little importance
Distortion of Map Projections

Summary
• Projections that minimize distortion of
shape are referred to as conformal
• Projections that minimize distortion of area
are referred to as equal-area
• Projections that minimize distortion of
distance are referred to as equidistant
• Projections that minimize distortion of
direction are referred to as true-direction
Projection Distortion

Some projections minimize distortions in some
of these properties at the expense of maximizing
errors in others

Others attempt to only moderately distort all of
these properties

Every projection has its own set of advantages
and disadvantages
Types of Map Projections

Conformal
• The scale of a map at any point on the map is the
same in any direction
• Meridians (longitude) and parallels (latitude) intersect
at right angles
• Shape is preserved locally on conformal maps
• Found mostly for maps used for measuring directions,
because they preserve directions around any given
point
• Examples - Lambert Conformal Conic & the Mercator
projections
Lambert Conformal Projection
URL: http://members.shaw.ca/quadibloc/maps/mco0301.htm
Mercator Projection
URL
http://math.rice.edu/~lanius/pres/map/maphis.html
Types of Projections

Equivalent (Equal-Area)
• Preserves the property of area
• All parts of the earth’s surface are shown with
the correct area
• Examples – Albers and Sinusoidal
Albers Projection
URL;
http://www.cnr.colostate.edu/class_info/nr502/lg2/projection_
descriptions/albers.html
Types of Map Projections

Equidistant
• Portrays distances from the center of the
projection to any other place on the map
• Useful only if distances are critical
• Infrequently used in GIS
• Simple conic & azimuthal equidistant
projections
The basis for three types of
map projections—cylindrical,
planar, and conic.
In each case a sheet of paper is
wrapped around the Earth, and
positions of objects on the Earth’s
surface are projected onto the paper.
The cylindrical projection is shown in
the tangent case, with the paper
touching the surface, but the planar and
conic projections are shown in the
secant case, where the paper cuts into
the surface.
(Reproduced by permission of Peter H. Dana)
Examples of some
common map
projections
The Mercator projection is a tangent
cylindrical type, shown here in its
familiar equatorial aspect (cylinder
wrapped around the equator).
The Lambert Conformal Conic
projection is a secant conic type. In
this instance, the cone onto which
the surface was projected
intersected the Earth along two lines
of latitude: 20 North and 60 North.
(A) The so-called unprojected or
Plate Carrée projection, a
tangent cylindrical projection
formed by using longitude as
x and latitude as y.
(B) A comparison of three
familiar projections of the United
States. The Lambert Conformal
Conic is the one most often
encountered when the United
States is projected alone and is
the only one of the three to
curve the parallels of latitude,
including the northern border on
the 49th Parallel.
Coordinate Systems
A Cartesian coordinate
system, defining the location
of the blue cross in terms of
two measured distances from
the origin, parallel to the two
axes
Coordinate Systems


Relative location - references to locations given
with respect to another place
Absolute location – a location in geographic
space given with respect to a known origin and
standard measurement system, such a
coordinate system
Locations to Numbers




We must choose a standard way to encode
locations on the earth
Locations on paper map can be given in map
millimeters or inches starting at the lower lefthand corner
Locations can then be given in (x, y) format –
east-west followed by north-south
Standard ways of listing coordinates are then
called coordinate systems
Locations to Numbers


A system with all the necessary components
to locate a position in 2- or 3-dimensional
space; that is, an origin, a type of unit
distance, and two axes
Many different coordinate systems, based on
a variety of geodetic datums, units,
projections, and reference systems in use
today
Coordinate Systems

Latitude and
Longitude
• Most common
coordinate system
• The Prime Meridian
and the Equator are
the reference planes
used to define latitude
and longitude
Hurvitz, P., University of Washington, CFR
250 Lecture Notes, 1999-2002
Latitude and Longitude

Start with a line connecting N and S pole
through the point
• The line is called a meridian


Latitude measures angle between the point and
the equator along the meridian
Longitude measures the angle on the equatorial
plane between the meridian of the point and the
central meridian (through Greenwich, England)
Coordinate Systems

Universal Transverse Mercator
• Earth divided into pole-to-pole zones
• Zones are each 6o of longitude wide
• First zone starts at 180oW, at the international date line
and runs east (180oW to 174oW)
• Final zone (zone 60) runs from 174oE to the date line
The system of zones of the Universal Transverse Mercator system. The zones are
identified at the top. Each zone is six degrees of longitude in width
(Reproduced by permission of Peter H. Dana)
Universal Transverse Mercator
URL:
http://www.colorado.edu/geography/gcraft/not
es/mapproj/mapproj_f.html
UTM Zones for the United States
URL:
http://mac.usgs.gov/mac/isb/pubs/factsheets
/fs07701.html
Northings and Eastings

Northings
• Earth ~40,000,000 m around, thus northings in a zone go from 0
to 10 million meters
• Southern hemisphere – 0 northing is the South Pole; 10 million
meter northing at equator
• Northern hemisphere – 0 northing at equator and 10 million
meter northing at North Pole

Eastings
• False origin established beyond the westerly limit of each
zone (about half a degree)
• Central meridian has an easting of 500,000m
• Advantages:
 Allows overlap between zones for mapping purposes
 Gives all eastings positive numbers
UTM Zones
Clarke, Getting Started with Geographic Information Systems,
prentice-Hall, 2001
UTM Advantages



Frequently used
Consistent for the globe
Provides a universal approach to accurate
georeferencing
UTM Disadvantages



Not used beyond 84oN & 80oS
Full georeference requires the zone number, easting and
northing (unless the area of the data base falls
completely within a zone)
Rectangular grid superimposed on zones defined by
meridians causes axes on adjacent zones to be skewed
with respect to each other
• problems arise in working across zone boundaries
• no simple mathematical relationship exists between coordinates
of one zone and an adjacent zone
Coordinate Systems

State Plane Coordinate System
• Based on both the transverse Mercator & the
Lambert conformal conic projections w/ units
in feet (metric versions now as well)
• Based upon a different map of each state
• E-W elongated states drawn on a Lambert
conformal conic projection
• N-S elongated states drawn on a transverse
Mercator projection
• Except Alaska – Lambert conformal conic,
transverse Mercator, & oblique Mercator
Coordinate Systems

State Plane Coordinate System
• Based upon a different map of each state
• E-W elongated states drawn on a Lambert conformal
conic projection
• N-S elongated states drawn on a transverse Mercator
projection
• Except Alaska – Lambert conformal conic, transverse
Mercator, & oblique Mercator
State Plane Coordinate System
URL:
http://www.pipeline.com/~rking/spc.htm
Coordinate Systems

State Plane Coordinate System
• Each zone has an arbitrarily determined origin that is
usually some given number of feet west and south of
the southernmost point on the map

Means that the eastings and northings all come out as
positive numbers

System then simply gives eastings and northings in feet
State Plane Advantages

Slightly more precise than UTM
• Foot rather than meter scale


SPCS can be more accurate over small areas
SPCS is used by surveyors all over the U.S.
State Plane Disadvantages


Lack of universality
Problems may arise at the boundaries of
projections
Military Grid Coordinate System

Adopted by U.S. Army in 1947

Uses a lettering & numbering system

West to east zones numbered from 1 to 60

Within zones, 8o strips of latitude lettered
from C (80o to 72o S) to X (72o to 84o N)
Military Grid Coordinate System
Clarke, Getting Started with Geographic
Information Systems, prentice-Hall,
2001
Set coordinates
to Lat/Long
Set coordinates
to State Plane
Set coordinates
to UTM